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Rectangle and Incircle Animation

Rectangle and Incircle Animation
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2017-04-21 01:19
CirclePolygonGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 1) Geometry Review Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1
This example demonstrates the geometric relationship between a rectangle and its incircle through animation. It involves core concepts like rectangle, incircle, similarity transformation, and proportional relationships. GeoGebra commands and objects used include Segment, Circle, Point, Angle, Rotate, Ray, Intersect, Line, Dilate, Vector, Polygon, Translate, If, Mirror. Suitable for high school geometry transformation and similarity studies, exploring properties of incircles and transformation patterns of rectangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Circle(D, (k * a)) → d
  5. Point(d) → E
  6. Segment(D, E) → e
  7. Circle(E, (k * b)) → f
  8. Angle(A, B, C) → α
  9. Rotate(D, α, E) → D'
  10. Angle(D, E, D') → β
  11. Ray(E, D') → g
  12. Intersect(f, g, 1) → F
  13. Angle(C, A, B) → γ
  14. Rotate(E, (-γ), D) → E'
  15. Angle(E', D, E) → δ
  16. Ray(D, E') → h
  17. Segment(D, E') → i
  18. Segment(E', E) → j
  19. Line(E, D') → l
  20. Line(E, D') → n
  21. Circle(D, (k * c)) → p
  22. Ray(D, E') → m
  23. Intersect(p, m, 1) → G
  24. Segment(E, G) → q
  25. Segment(D, G) → r
  26. Dilate(D, If[0 < s ≤ 1, 1 - s], A) → D'_1
  27. Vector(D, D'_1) → u
  28. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  29. Polygon(D, E, G) → poly2, g_1, d_1, e_1
  30. Translate(D, u) → D'_2
  31. Translate(E, u) → E'_1
  32. Translate(G, u) → G'
  33. Polygon(D'_2, E'_1, G') → poly2', g', d'_2, e'_1
  34. Vector(D, A) → v
  35. Translate(D, v) → D'_3
  36. Translate(E, v) → E'_2
  37. Translate(G, v) → G'_1
  38. Polygon(D'_3, E'_2, G'_1) → poly2'_1, g'_1, d'_3, e'_2
  39. Segment(D'_1, G') → t
  40. Segment(E'_1, D'_1) → h_1
  41. Segment(A, G'_1) → i_1
  42. Segment(G'_1, E'_2) → j_1
  43. Segment(E'_2, A) → k_1
  44. Angle(C, A, E'_2) → ε
  45. If(ε > γ, ε - γ, γ - ε) → ζ
  46. Rotate(D'_3, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → H
  47. Rotate(E'_2, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → I
  48. Rotate(G'_1, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → J
  49. Polygon(H, I, J) → poly3, j_2, h_2, i_2
  50. Segment(A, J) → l_1
  51. Segment(A, I) → m_1
  52. Segment(I, J) → n_1
  53. Dilate(J, If[2 < s ≤ 3, 3 - s, 0], C) → J'
  54. Dilate(I, If[2 < s ≤ 3, 3 - s, 0], B) → I'
  55. Segment(I', J') → p_1
  56. Angle(A, I, J) → θ
  57. Angle(D'_2, E'_1, G') → ι
  58. Angle(J, A, I) → λ
  59. Angle(G', D'_1, E'_1) → μ
  60. Polygon(A, J', I') → poly4, i', a_2, j'
  61. Segment(G'_1, E'_2) → q_1
  62. Segment(G', E'_1) → f_1
  63. Rotate(D'_3, ((s - 1) * ζ), A) → K
  64. Rotate(D'_3, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → L
  65. Rotate(E'_2, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → M
  66. Rotate(G'_1, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → N
  67. Polygon(L, M, N) → poly5, n_2, l_2, m_2
  68. Dilate(M, If[2 < s ≤ 3, 3 - s, 0], B) → M'
  69. Dilate(N, If[2 < s ≤ 3, 3 - s, 0], C) → N'
  70. Segment(M', N') → r_1
  71. Polygon(A, M', N') → poly6, n', a_3, m'
  72. Angle(A, M', N') → ο
  73. Angle(A, M, N) → ρ
  74. Segment(A, M) → t_1
  75. Segment(M, N) → b_2
  76. Segment(A, N) → c_2
  77. Angle(B, A, C) → σ
  78. Angle(G, E, D) → τ
  79. Angle(N, M, A) → υ
  80. Angle(N', M', A) → ϕ
  81. Line(E, G) → s_1
  82. Mirror(D, q) → D'_4
  83. Mirror(E, q) → E'_3
  84. Mirror(G, q) → G'_2
  85. Polygon(D'_4, E'_3, G'_2) → poly2'_2, g'_2, d'_4, e'_3
  86. Segment(E, D'_4) → f_2
  87. Segment(D'_4, G) → g_2